Bayesian Dose-Finding Trial Simulation

Introduction

This document provides an interactive way to run the Bayesian dose-finding trial simulation. You can modify the simulation parameters in the “Configuration” section and then run the code chunks to see the results.

Setup

This chunk loads the necessary libraries and source files.

library(knitr)
library(ggplot2)

# Use absolute paths
project_root <- "/Users/jz/Development/DoseFinding"
cat("Project root:", project_root, "\n")

Project root: /Users/jz/Development/DoseFinding 

# Source core files
source(file.path(project_root, "src/core/config.R"))

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Iso 0.0-21

     An "infelicity" in the function ufit() (whereby 
     it was all too easy to conflate the location of 
     the mode with its index in the entries of the 
     "x" argument) has been corrected.  To this end, 
     ufit() now has arguments "lmode" (the location 
     of the mode), and "imode" (its index).  At most 
     one of these arguments should be specified.  See 
     the help for ufit().

source(file.path(project_root, "src/utils/helpers.R"))
source(file.path(project_root, "src/utils/plotting_extensions.R"))
source(file.path(project_root, "src/core/simulate_data.R"))
source(file.path(project_root, "src/core/model_utils.R"))
source(file.path(project_root, "src/decision/dose_decision.R"))
source(file.path(project_root, "src/core/main.R"))

Configuration

Modify the simulation parameters in this section. I have adjusted these values to create a more dynamic scenario where multiple doses are likely to be admissible in the early stages.

# Trial configuration
trial_config <- list(
  dose_levels = c(1, 2, 3, 4, 5),
  n_stages = 5,
  cohort_size = 15,
  phi_T = 0.35, # Toxicity threshold (increased slightly)
  c_T = 0.5,   
  phi_E = 0.1, # Efficacy threshold (increased slightly)
  c_E = 0.5,   
  phi_I = 0.20, # Immune response threshold
  c_I = 0.5,   
  # PoC parameters
  c_poc = 0.9,
  delta_poc = 0.8,  # Threshold for PoC comparison
  # Early termination parameters
  enable_early_termination = TRUE,
  log_early_termination = TRUE
)
#cohort size may vary on diff stage (future work)

# Data simulation parameters (designed for a more interesting trial)
p_YI <- c(0.10, 0.30, 0.50, 0.60, 0.70) # Immune response probability

p_YT_given_I <- matrix(c(
  # I=0 (No Immune Response)
  0.05, 0.10, 0.12, 0.18, 0.25,
  # I=1 (Immune Response)
  0.08, 0.12, 0.15, 0.25, 0.35
), nrow = 5, ncol = 2)

p_YE_given_I <- matrix(c(
  # I=0 (No Immune Response)
  0.10, 0.20, 0.35, 0.45, 0.50, 
  # I=1 (Immune Response)
  0.30, 0.50, 0.70, 0.80, 0.75  
), nrow = 5, ncol = 2)

rho0 <- 1.5
rho1 <- 2

# Utility table
# Rows: Efficacy (0, 1)
# Columns: Toxicity (0, 1)
# Slices: Immune Response (0, 1)
utility_table <- array(0, dim = c(2, 2, 2), dimnames = list(
  E = c(0, 1),
  T = c(0, 1),
  I = c(0, 1)
))

utility_table[1, 1, 1] <- 0   # E=0, T=0, I=0
utility_table[2, 1, 1] <- 80  # E=1, T=0, I=0
utility_table[1, 2, 1] <- 0   # E=0, T=1, I=0
utility_table[2, 2, 1] <- 30  # E=1, T=1, I=0

utility_table[1, 1, 2] <- 10  # E=0, T=0, I=1
utility_table[2, 1, 2] <- 100 # E=1, T=0, I=1
utility_table[1, 2, 2] <- 0   # E=0, T=1, I=1
utility_table[2, 2, 2] <- 40  # E=1, T=1, I=1

trial_config$utility_table <- utility_table

Simulation

This chunk runs the multi-stage trial simulation by calling the run_trial_simulation function. The simulation follows the workflow specified in TRIAL_DESIGN.md:

1. Stage 1: Equal randomization to all dose levels
2. Interim Analysis: Update admissible set based on posterior probabilities
3. Adaptive Randomization: Allocate patients based on utility scores
4. Early Termination Check: Terminate if admissible set is empty
5. Final Selection: Choose OD with highest utility from admissible set + PoC validation

results <- run_trial_simulation(trial_config, p_YI, p_YT_given_I, p_YE_given_I, rho0, rho1)

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.238 0.272 0.338 0.358 0.412 
Summary: Efficacy marginal means: 0.321 0.41 0.468 0.55 0.782 
Summary: Immune response means: 0.159 0.24 0.479 0.517 0.81 
Dose 1 : P(Tox <  0.35 ) =  0.9 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.33 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  0.82 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.56 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.58 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.99 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.47 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.99 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.159 
  Toxicity given I=0 (π_T|I=0): 0.22 
  Toxicity given I=1 (π_T|I=1): 0.34 
  Efficacy given I=0 (π_E|I=0): 0.3 
  Efficacy given I=1 (π_E|I=1): 0.43 
  Probability distributions:
    P(T=0|I=0): 0.78 P(T=1|I=0): 0.22 
    P(T=0|I=1): 0.66 P(T=1|I=1): 0.34 
    P(E=0|I=0): 0.7 P(E=1|I=0): 0.3 
    P(E=0|I=1): 0.57 P(E=1|I=1): 0.43 
  Expected utility given I=0: 20.69 
  Expected utility given I=1: 37.97 
  Total expected utility: 23.43 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.24 
  Toxicity given I=0 (π_T|I=0): 0.238 
  Toxicity given I=1 (π_T|I=1): 0.379 
  Efficacy given I=0 (π_E|I=0): 0.382 
  Efficacy given I=1 (π_E|I=1): 0.501 
  Probability distributions:
    P(T=0|I=0): 0.762 P(T=1|I=0): 0.238 
    P(T=0|I=1): 0.621 P(T=1|I=1): 0.379 
    P(E=0|I=0): 0.618 P(E=1|I=0): 0.382 
    P(E=0|I=1): 0.499 P(E=1|I=1): 0.501 
  Expected utility given I=0: 26.04 
  Expected utility given I=1: 41.85 
  Total expected utility: 29.84 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.479 
  Toxicity given I=0 (π_T|I=0): 0.282 
  Toxicity given I=1 (π_T|I=1): 0.398 
  Efficacy given I=0 (π_E|I=0): 0.387 
  Efficacy given I=1 (π_E|I=1): 0.556 
  Probability distributions:
    P(T=0|I=0): 0.718 P(T=1|I=0): 0.282 
    P(T=0|I=1): 0.602 P(T=1|I=1): 0.398 
    P(E=0|I=0): 0.613 P(E=1|I=0): 0.387 
    P(E=0|I=1): 0.444 P(E=1|I=1): 0.556 
  Expected utility given I=0: 25.51 
  Expected utility given I=1: 45 
  Total expected utility: 34.85 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.517 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.404 
  Efficacy given I=0 (π_E|I=0): 0.403 
  Efficacy given I=1 (π_E|I=1): 0.689 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.596 P(T=1|I=1): 0.404 
    P(E=0|I=0): 0.597 P(E=1|I=0): 0.403 
    P(E=0|I=1): 0.311 P(E=1|I=1): 0.689 
  Expected utility given I=0: 26.01 
  Expected utility given I=1: 54.04 
  Total expected utility: 40.49 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.81 
  Toxicity given I=0 (π_T|I=0): 0.377 
  Toxicity given I=1 (π_T|I=1): 0.42 
  Efficacy given I=0 (π_E|I=0): 0.56 
  Efficacy given I=1 (π_E|I=1): 0.835 
  Probability distributions:
    P(T=0|I=0): 0.623 P(T=1|I=0): 0.377 
    P(T=0|I=1): 0.58 P(T=1|I=1): 0.42 
    P(E=0|I=0): 0.44 P(E=1|I=0): 0.56 
    P(E=0|I=1): 0.165 P(E=1|I=1): 0.835 
  Expected utility given I=0: 34.24 
  Expected utility given I=1: 63.45 
  Total expected utility: 57.89 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.159 |    0.220 |    0.340 |    0.300 |    0.430 |   20.7 |   38.0 |    23.4
   2 |  0.240 |    0.238 |    0.379 |    0.382 |    0.501 |   26.0 |   41.8 |    29.8
   3 |  0.479 |    0.282 |    0.398 |    0.387 |    0.556 |   25.5 |   45.0 |    34.8
   4 |  0.517 |    0.309 |    0.404 |    0.403 |    0.689 |   26.0 |   54.0 |    40.5
   5 |  0.810 |    0.377 |    0.420 |    0.560 |    0.835 |   34.2 |   63.5 |    57.9

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.4612858 0.5387142 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.147 0.17 0.258 0.308 0.375 
Summary: Efficacy marginal means: 0.289 0.345 0.406 0.535 0.774 
Summary: Immune response means: 0.158 0.272 0.544 0.564 0.815 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.32 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.71 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.91 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.48 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.158 
  Toxicity given I=0 (π_T|I=0): 0.126 
  Toxicity given I=1 (π_T|I=1): 0.258 
  Efficacy given I=0 (π_E|I=0): 0.278 
  Efficacy given I=1 (π_E|I=1): 0.35 
  Probability distributions:
    P(T=0|I=0): 0.874 P(T=1|I=0): 0.126 
    P(T=0|I=1): 0.742 P(T=1|I=1): 0.258 
    P(E=0|I=0): 0.722 P(E=1|I=0): 0.278 
    P(E=0|I=1): 0.65 P(E=1|I=1): 0.35 
  Expected utility given I=0: 20.48 
  Expected utility given I=1: 34.44 
  Total expected utility: 22.69 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.272 
  Toxicity given I=0 (π_T|I=0): 0.13 
  Toxicity given I=1 (π_T|I=1): 0.277 
  Efficacy given I=0 (π_E|I=0): 0.332 
  Efficacy given I=1 (π_E|I=1): 0.382 
  Probability distributions:
    P(T=0|I=0): 0.87 P(T=1|I=0): 0.13 
    P(T=0|I=1): 0.723 P(T=1|I=1): 0.277 
    P(E=0|I=0): 0.668 P(E=1|I=0): 0.332 
    P(E=0|I=1): 0.618 P(E=1|I=1): 0.382 
  Expected utility given I=0: 24.37 
  Expected utility given I=1: 36.3 
  Total expected utility: 27.62 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.544 
  Toxicity given I=0 (π_T|I=0): 0.179 
  Toxicity given I=1 (π_T|I=1): 0.323 
  Efficacy given I=0 (π_E|I=0): 0.333 
  Efficacy given I=1 (π_E|I=1): 0.467 
  Probability distributions:
    P(T=0|I=0): 0.821 P(T=1|I=0): 0.179 
    P(T=0|I=1): 0.677 P(T=1|I=1): 0.323 
    P(E=0|I=0): 0.667 P(E=1|I=0): 0.333 
    P(E=0|I=1): 0.533 P(E=1|I=1): 0.467 
  Expected utility given I=0: 23.63 
  Expected utility given I=1: 41.24 
  Total expected utility: 33.2 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.564 
  Toxicity given I=0 (π_T|I=0): 0.248 
  Toxicity given I=1 (π_T|I=1): 0.355 
  Efficacy given I=0 (π_E|I=0): 0.364 
  Efficacy given I=1 (π_E|I=1): 0.669 
  Probability distributions:
    P(T=0|I=0): 0.752 P(T=1|I=0): 0.248 
    P(T=0|I=1): 0.645 P(T=1|I=1): 0.355 
    P(E=0|I=0): 0.636 P(E=1|I=0): 0.364 
    P(E=0|I=1): 0.331 P(E=1|I=1): 0.669 
  Expected utility given I=0: 24.6 
  Expected utility given I=1: 54.79 
  Total expected utility: 41.62 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.815 
  Toxicity given I=0 (π_T|I=0): 0.343 
  Toxicity given I=1 (π_T|I=1): 0.382 
  Efficacy given I=0 (π_E|I=0): 0.551 
  Efficacy given I=1 (π_E|I=1): 0.825 
  Probability distributions:
    P(T=0|I=0): 0.657 P(T=1|I=0): 0.343 
    P(T=0|I=1): 0.618 P(T=1|I=1): 0.382 
    P(E=0|I=0): 0.449 P(E=1|I=0): 0.551 
    P(E=0|I=1): 0.175 P(E=1|I=1): 0.825 
  Expected utility given I=0: 34.6 
  Expected utility given I=1: 64.65 
  Total expected utility: 59.09 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.158 |    0.126 |    0.258 |    0.278 |    0.350 |   20.5 |   34.4 |    22.7
   2 |  0.272 |    0.130 |    0.277 |    0.332 |    0.382 |   24.4 |   36.3 |    27.6
   3 |  0.544 |    0.179 |    0.323 |    0.333 |    0.467 |   23.6 |   41.2 |    33.2
   4 |  0.564 |    0.248 |    0.355 |    0.364 |    0.669 |   24.6 |   54.8 |    41.6
   5 |  0.815 |    0.343 |    0.382 |    0.551 |    0.825 |   34.6 |   64.6 |    59.1

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.2695908 0.3241299 0.4062793 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.124 0.14 0.203 0.224 0.333 
Summary: Efficacy marginal means: 0.304 0.373 0.449 0.528 0.768 
Summary: Immune response means: 0.178 0.321 0.51 0.517 0.809 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.4 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.96 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.62 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.178 
  Toxicity given I=0 (π_T|I=0): 0.11 
  Toxicity given I=1 (π_T|I=1): 0.19 
  Efficacy given I=0 (π_E|I=0): 0.294 
  Efficacy given I=1 (π_E|I=1): 0.349 
  Probability distributions:
    P(T=0|I=0): 0.89 P(T=1|I=0): 0.11 
    P(T=0|I=1): 0.81 P(T=1|I=1): 0.19 
    P(E=0|I=0): 0.706 P(E=1|I=0): 0.294 
    P(E=0|I=1): 0.651 P(E=1|I=1): 0.349 
  Expected utility given I=0: 21.9 
  Expected utility given I=1: 36.14 
  Total expected utility: 24.43 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.321 
  Toxicity given I=0 (π_T|I=0): 0.112 
  Toxicity given I=1 (π_T|I=1): 0.202 
  Efficacy given I=0 (π_E|I=0): 0.371 
  Efficacy given I=1 (π_E|I=1): 0.379 
  Probability distributions:
    P(T=0|I=0): 0.888 P(T=1|I=0): 0.112 
    P(T=0|I=1): 0.798 P(T=1|I=1): 0.202 
    P(E=0|I=0): 0.629 P(E=1|I=0): 0.371 
    P(E=0|I=1): 0.621 P(E=1|I=1): 0.379 
  Expected utility given I=0: 27.59 
  Expected utility given I=1: 38.24 
  Total expected utility: 31.01 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.51 
  Toxicity given I=0 (π_T|I=0): 0.162 
  Toxicity given I=1 (π_T|I=1): 0.242 
  Efficacy given I=0 (π_E|I=0): 0.392 
  Efficacy given I=1 (π_E|I=1): 0.503 
  Probability distributions:
    P(T=0|I=0): 0.838 P(T=1|I=0): 0.162 
    P(T=0|I=1): 0.758 P(T=1|I=1): 0.242 
    P(E=0|I=0): 0.608 P(E=1|I=0): 0.392 
    P(E=0|I=1): 0.497 P(E=1|I=1): 0.503 
  Expected utility given I=0: 28.15 
  Expected utility given I=1: 46.75 
  Total expected utility: 37.64 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.517 
  Toxicity given I=0 (π_T|I=0): 0.178 
  Toxicity given I=1 (π_T|I=1): 0.266 
  Efficacy given I=0 (π_E|I=0): 0.427 
  Efficacy given I=1 (π_E|I=1): 0.623 
  Probability distributions:
    P(T=0|I=0): 0.822 P(T=1|I=0): 0.178 
    P(T=0|I=1): 0.734 P(T=1|I=1): 0.266 
    P(E=0|I=0): 0.573 P(E=1|I=0): 0.427 
    P(E=0|I=1): 0.377 P(E=1|I=1): 0.623 
  Expected utility given I=0: 30.33 
  Expected utility given I=1: 55.14 
  Total expected utility: 43.15 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.809 
  Toxicity given I=0 (π_T|I=0): 0.302 
  Toxicity given I=1 (π_T|I=1): 0.339 
  Efficacy given I=0 (π_E|I=0): 0.564 
  Efficacy given I=1 (π_E|I=1): 0.818 
  Probability distributions:
    P(T=0|I=0): 0.698 P(T=1|I=0): 0.302 
    P(T=0|I=1): 0.661 P(T=1|I=1): 0.339 
    P(E=0|I=0): 0.436 P(E=1|I=0): 0.564 
    P(E=0|I=1): 0.182 P(E=1|I=1): 0.818 
  Expected utility given I=0: 36.63 
  Expected utility given I=1: 66.34 
  Total expected utility: 60.66 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.178 |    0.110 |    0.190 |    0.294 |    0.349 |   21.9 |   36.1 |    24.4
   2 |  0.321 |    0.112 |    0.202 |    0.371 |    0.379 |   27.6 |   38.2 |    31.0
   3 |  0.510 |    0.162 |    0.242 |    0.392 |    0.503 |   28.2 |   46.8 |    37.6
   4 |  0.517 |    0.178 |    0.266 |    0.427 |    0.623 |   30.3 |   55.1 |    43.1
   5 |  0.809 |    0.302 |    0.339 |    0.564 |    0.818 |   36.6 |   66.3 |    60.7

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.1798065 0.2182409 0.2501857 0.3517669 

--- Stage 4 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.105 0.119 0.178 0.189 0.235 
Summary: Efficacy marginal means: 0.286 0.337 0.471 0.534 0.801 
Summary: Immune response means: 0.177 0.324 0.525 0.526 0.799 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.41 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.89 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.177 
  Toxicity given I=0 (π_T|I=0): 0.092 
  Toxicity given I=1 (π_T|I=1): 0.166 
  Efficacy given I=0 (π_E|I=0): 0.278 
  Efficacy given I=1 (π_E|I=1): 0.325 
  Probability distributions:
    P(T=0|I=0): 0.908 P(T=1|I=0): 0.092 
    P(T=0|I=1): 0.834 P(T=1|I=1): 0.166 
    P(E=0|I=0): 0.722 P(E=1|I=0): 0.278 
    P(E=0|I=1): 0.675 P(E=1|I=1): 0.325 
  Expected utility given I=0: 20.93 
  Expected utility given I=1: 34.9 
  Total expected utility: 23.4 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.324 
  Toxicity given I=0 (π_T|I=0): 0.093 
  Toxicity given I=1 (π_T|I=1): 0.175 
  Efficacy given I=0 (π_E|I=0): 0.335 
  Efficacy given I=1 (π_E|I=1): 0.343 
  Probability distributions:
    P(T=0|I=0): 0.907 P(T=1|I=0): 0.093 
    P(T=0|I=1): 0.825 P(T=1|I=1): 0.175 
    P(E=0|I=0): 0.665 P(E=1|I=0): 0.335 
    P(E=0|I=1): 0.657 P(E=1|I=1): 0.343 
  Expected utility given I=0: 25.21 
  Expected utility given I=1: 36.16 
  Total expected utility: 28.76 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.525 
  Toxicity given I=0 (π_T|I=0): 0.131 
  Toxicity given I=1 (π_T|I=1): 0.221 
  Efficacy given I=0 (π_E|I=0): 0.349 
  Efficacy given I=1 (π_E|I=1): 0.581 
  Probability distributions:
    P(T=0|I=0): 0.869 P(T=1|I=0): 0.131 
    P(T=0|I=1): 0.779 P(T=1|I=1): 0.221 
    P(E=0|I=0): 0.651 P(E=1|I=0): 0.349 
    P(E=0|I=1): 0.419 P(E=1|I=1): 0.581 
  Expected utility given I=0: 25.67 
  Expected utility given I=1: 53.67 
  Total expected utility: 40.36 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.526 
  Toxicity given I=0 (π_T|I=0): 0.139 
  Toxicity given I=1 (π_T|I=1): 0.235 
  Efficacy given I=0 (π_E|I=0): 0.359 
  Efficacy given I=1 (π_E|I=1): 0.691 
  Probability distributions:
    P(T=0|I=0): 0.861 P(T=1|I=0): 0.139 
    P(T=0|I=1): 0.765 P(T=1|I=1): 0.235 
    P(E=0|I=0): 0.641 P(E=1|I=0): 0.359 
    P(E=0|I=1): 0.309 P(E=1|I=1): 0.691 
  Expected utility given I=0: 26.23 
  Expected utility given I=1: 61.74 
  Total expected utility: 44.9 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.799 
  Toxicity given I=0 (π_T|I=0): 0.205 
  Toxicity given I=1 (π_T|I=1): 0.242 
  Efficacy given I=0 (π_E|I=0): 0.442 
  Efficacy given I=1 (π_E|I=1): 0.891 
  Probability distributions:
    P(T=0|I=0): 0.795 P(T=1|I=0): 0.205 
    P(T=0|I=1): 0.758 P(T=1|I=1): 0.242 
    P(E=0|I=0): 0.558 P(E=1|I=0): 0.442 
    P(E=0|I=1): 0.109 P(E=1|I=1): 0.891 
  Expected utility given I=0: 30.8 
  Expected utility given I=1: 76.98 
  Total expected utility: 67.69 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.177 |    0.092 |    0.166 |    0.278 |    0.325 |   20.9 |   34.9 |    23.4
   2 |  0.324 |    0.093 |    0.175 |    0.335 |    0.343 |   25.2 |   36.2 |    28.8
   3 |  0.525 |    0.131 |    0.221 |    0.349 |    0.581 |   25.7 |   53.7 |    40.4
   4 |  0.526 |    0.139 |    0.235 |    0.359 |    0.691 |   26.2 |   61.7 |    44.9
   5 |  0.799 |    0.205 |    0.242 |    0.442 |    0.891 |   30.8 |   77.0 |    67.7

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.1582726 0.2221118 0.2471072 0.3725084 

--- Stage 5 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.092 0.107 0.163 0.177 0.219 
Summary: Efficacy marginal means: 0.277 0.319 0.491 0.556 0.745 
Summary: Immune response means: 0.173 0.343 0.533 0.534 0.641 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.39 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.94 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.96 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.173 
  Toxicity given I=0 (π_T|I=0): 0.08 
  Toxicity given I=1 (π_T|I=1): 0.15 
  Efficacy given I=0 (π_E|I=0): 0.27 
  Efficacy given I=1 (π_E|I=1): 0.306 
  Probability distributions:
    P(T=0|I=0): 0.92 P(T=1|I=0): 0.08 
    P(T=0|I=1): 0.85 P(T=1|I=1): 0.15 
    P(E=0|I=0): 0.73 P(E=1|I=0): 0.27 
    P(E=0|I=1): 0.694 P(E=1|I=1): 0.306 
  Expected utility given I=0: 20.51 
  Expected utility given I=1: 33.78 
  Total expected utility: 22.8 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.343 
  Toxicity given I=0 (π_T|I=0): 0.081 
  Toxicity given I=1 (π_T|I=1): 0.157 
  Efficacy given I=0 (π_E|I=0): 0.318 
  Efficacy given I=1 (π_E|I=1): 0.322 
  Probability distributions:
    P(T=0|I=0): 0.919 P(T=1|I=0): 0.081 
    P(T=0|I=1): 0.843 P(T=1|I=1): 0.157 
    P(E=0|I=0): 0.682 P(E=1|I=0): 0.318 
    P(E=0|I=1): 0.678 P(E=1|I=1): 0.322 
  Expected utility given I=0: 24.15 
  Expected utility given I=1: 34.88 
  Total expected utility: 27.83 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.533 
  Toxicity given I=0 (π_T|I=0): 0.114 
  Toxicity given I=1 (π_T|I=1): 0.205 
  Efficacy given I=0 (π_E|I=0): 0.327 
  Efficacy given I=1 (π_E|I=1): 0.634 
  Probability distributions:
    P(T=0|I=0): 0.886 P(T=1|I=0): 0.114 
    P(T=0|I=1): 0.795 P(T=1|I=1): 0.205 
    P(E=0|I=0): 0.673 P(E=1|I=0): 0.327 
    P(E=0|I=1): 0.366 P(E=1|I=1): 0.634 
  Expected utility given I=0: 24.33 
  Expected utility given I=1: 58.52 
  Total expected utility: 42.55 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.534 
  Toxicity given I=0 (π_T|I=0): 0.119 
  Toxicity given I=1 (π_T|I=1): 0.228 
  Efficacy given I=0 (π_E|I=0): 0.336 
  Efficacy given I=1 (π_E|I=1): 0.747 
  Probability distributions:
    P(T=0|I=0): 0.881 P(T=1|I=0): 0.119 
    P(T=0|I=1): 0.772 P(T=1|I=1): 0.228 
    P(E=0|I=0): 0.664 P(E=1|I=0): 0.336 
    P(E=0|I=1): 0.253 P(E=1|I=1): 0.747 
  Expected utility given I=0: 24.89 
  Expected utility given I=1: 66.41 
  Total expected utility: 47.06 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.641 
  Toxicity given I=0 (π_T|I=0): 0.201 
  Toxicity given I=1 (π_T|I=1): 0.229 
  Efficacy given I=0 (π_E|I=0): 0.576 
  Efficacy given I=1 (π_E|I=1): 0.84 
  Probability distributions:
    P(T=0|I=0): 0.799 P(T=1|I=0): 0.201 
    P(T=0|I=1): 0.771 P(T=1|I=1): 0.229 
    P(E=0|I=0): 0.424 P(E=1|I=0): 0.576 
    P(E=0|I=1): 0.16 P(E=1|I=1): 0.84 
  Expected utility given I=0: 40.29 
  Expected utility given I=1: 73.67 
  Total expected utility: 61.69 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.173 |    0.080 |    0.150 |    0.270 |    0.306 |   20.5 |   33.8 |    22.8
   2 |  0.343 |    0.081 |    0.157 |    0.318 |    0.322 |   24.2 |   34.9 |    27.8
   3 |  0.533 |    0.114 |    0.205 |    0.327 |    0.634 |   24.3 |   58.5 |    42.5
   4 |  0.534 |    0.119 |    0.228 |    0.336 |    0.747 |   24.9 |   66.4 |    47.1
   5 |  0.641 |    0.201 |    0.229 |    0.576 |    0.840 |   40.3 |   73.7 |    61.7

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.440±0.103, Πᵢⱼ=0.732±0.101, PoC=0.854
PoC calculation for dose 3: Πᵢ=0.503±0.091, Πᵢⱼ=0.732±0.101, PoC=0.759
PoC calculation for dose 4: Πᵢ=0.508±0.101, Πᵢⱼ=0.732±0.101, PoC=0.724
PoC calculation for dose 5: Πᵢ=0.732±0.101, Πᵢⱼ=0.732±0.101, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0.854 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 3 4 5 
Utilities: 27.83 42.55 47.06 61.69 
Selected dose: 5 
Selected utility: 61.69 
PoC validated: FALSE 
Max PoC probability: 0.854 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

Results

This chunk prints the final optimal dose and displays the plots.

# Print final results
cat("
--- Final Results ---
")

--- Final Results ---

if (results$terminated_early) {
  cat("Trial terminated early at stage:", results$termination_stage, "
")
  cat("Reason:", results$termination_reason, "
")
  cat("No Optimal Dose selected
")
} else {
  cat("Final OD:", results$final_od, "
")
  cat("Final utility:", round(results$final_utility, 2), "
")
  cat("PoC validated:", results$poc_validated, "
")
  cat("PoC probability:", round(results$poc_probability, 3), "
")
  cat("Selection reason:", results$selection_reason, "
")
}

Final OD: 5 
Final utility: 61.69 
PoC validated: FALSE 
PoC probability: 0.854 
Selection reason: PoC threshold not met, but selecting best available dose 

# Plot final results and save them with modern styling
plot_posterior_summary(results$posterior_summaries$imm, title = "Immune Response vs Dose (PAVA Adjusted)", file_path = "results/plots/immune_response_refactored.png", style = "modern")

plot_posterior_summary(results$posterior_summaries$tox, title = "Toxicity Rate by Dose and Immune Status", group_col = "Y_I", file_path = "results/plots/toxicity_refactored.png", style = "modern")

plot_posterior_summary(results$posterior_summaries$eff, title = "Efficacy Rate by Dose and Immune Status", group_col = "Y_I", file_path = "results/plots/efficacy_refactored.png", style = "modern")

# Create dose-response curves similar to reference code
cat("\n=== Creating Dose-Response Curves ===\n")

=== Creating Dose-Response Curves ===

# Extract true probabilities for dose-response curves
true_toxicity <- p_YT_given_I[,1] * (1 - p_YI) + p_YT_given_I[,2] * p_YI
true_efficacy <- p_YE_given_I[,1] * (1 - p_YI) + p_YE_given_I[,2] * p_YI
true_utility <- results$final_utility_by_dose

# Create dose-response curves plot
dose_response_plot <- plot_dose_response_curves(
  toxicity_data = true_toxicity,
  efficacy_data = true_efficacy,
  utility_data = true_utility,
  title = "True Dose-Response Curves",
  file_path = "results/plots/dose_response_curves.png"
)

Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_line()`).

Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).

print(dose_response_plot)

Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_line()`).
Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).

# Plot allocation probabilities over time with modern styling
p_alloc_time <- ggplot(results$all_alloc_probs, aes(x = Stage, y = Prob, color = factor(Dose))) +
  geom_line(linewidth = 1) +
  geom_point(size = 3) +
  labs(title = "Allocation Probabilities Over Time", 
       x = "Stage", y = "Allocation Probability", 
       color = "Dose Level") +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.line = element_line(color = "black"))
print(p_alloc_time)

# Visualize participant allocation with better formatting
# Count participants per dose level and stage
allocation_summary <- results$all_data %>%
  group_by(d, stage) %>%
  summarise(n_participants = n(), .groups = 'drop') %>%
  mutate(d = factor(d), stage = factor(stage, levels = 1:5, labels = paste("Stage", 1:5)))

# Plot 1: Allocation by dose level and stage with modern styling
p_alloc <- ggplot(allocation_summary, aes(x = d, y = n_participants, fill = stage)) +
  geom_bar(stat = "identity", position = "dodge", width = 0.7, color = "black") +
  labs(title = "Participant Allocation by Dose Level and Stage", 
       x = "Dose Level", y = "Number of Participants",
       subtitle = paste("Total participants:", sum(allocation_summary$n_participants))) +
  scale_fill_manual(name = "Stage", values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
        axis.text = element_text(size = 12),
        axis.title = element_text(size = 12),
        axis.line = element_line(color = "black"))
print(p_alloc)

# Plot 2: Cumulative allocation over stages
cumulative_summary <- allocation_summary %>%
  group_by(d) %>%
  mutate(cumulative_participants = cumsum(n_participants)) %>%
  ungroup()

p_cumulative <- ggplot(cumulative_summary, aes(x = stage, y = cumulative_participants, color = d, group = d)) +
  geom_line(linewidth = 1.5) +
  geom_point(size = 3) +
  labs(title = "Cumulative Participant Allocation Over Stages", 
       x = "Stage", y = "Cumulative Number of Participants",
       color = "Dose Level",
       subtitle = paste("Final total participants:", sum(allocation_summary$n_participants))) +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
        axis.text = element_text(size = 12),
        axis.title = element_text(size = 12),
        axis.line = element_line(color = "black"))
print(p_cumulative)

# Print summary statistics
cat("\n=== ALLOCATION SUMMARY ===\n")

=== ALLOCATION SUMMARY ===

cat("Total participants:", sum(allocation_summary$n_participants), "\n")

Total participants: 75 

cat("Participants per stage:\n")

Participants per stage:

stage_totals <- allocation_summary %>%
  group_by(stage) %>%
  summarise(total = sum(n_participants), .groups = 'drop')
for(i in 1:nrow(stage_totals)) {
  cat("  Stage", i, ":", stage_totals$total[i], "participants\n")
}

  Stage 1 : 15 participants
  Stage 2 : 15 participants
  Stage 3 : 15 participants
  Stage 4 : 15 participants
  Stage 5 : 15 participants

Method Comparison Analysis

This section creates comparison plots similar to the reference code, showing how different methods or parameter settings would perform.

# Create example data for method comparison (similar to reference code)
cat("\n=== Creating Method Comparison Plots ===\n")

=== Creating Method Comparison Plots ===

# Simulate different method performances
methods <- c("Current", "Proposed", "Reference")
scenarios <- c("Scenario 1", "Scenario 2", "Scenario 3")

# OBD Selection Rate Comparison
obd_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
obd_data$obd_rate <- c(45, 60, 55, 70, 65, 50, 80, 85, 75)

# Create OBD selection plot
p_obd <- plot_method_comparison_bars(
  obd_data,
  x_var = "scenario", y_var = "obd_rate", fill_var = "method",
  title = "OBD Selection Rate Comparison",
  y_label = "OBD Selection (%)",
  limits = c(0, 100),
  file_path = "results/plots/obd_selection_comparison.png"
)

Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
ℹ Please use tidy evaluation idioms with `aes()`.
ℹ See also `vignette("ggplot2-in-packages")` for more information.

print(p_obd)

# Sample Size Comparison
sample_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
sample_data$avg_n <- c(25, 20, 30, 22, 18, 28, 18, 15, 25)

# Create sample size plot
p_sample <- plot_method_comparison_bars(
  sample_data,
  x_var = "scenario", y_var = "avg_n", fill_var = "method",
  title = "Average Sample Size Comparison",
  y_label = "Average Sample Size",
  limits = c(0, 35),
  file_path = "results/plots/sample_size_comparison.png"
)
print(p_sample)

# Safety (Overdose) Comparison
safety_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
safety_data$overdose_pct <- c(15, 10, 20, 12, 8, 18, 8, 5, 15)

# Create safety plot
p_safety <- plot_method_comparison_bars(
  safety_data,
  x_var = "scenario", y_var = "overdose_pct", fill_var = "method",
  title = "Overdose Patient Percentage",
  y_label = "Overdose Pts (%)",
  limits = c(0, 25),
  file_path = "results/plots/safety_comparison.png"
)
print(p_safety)

cat("✅ Method comparison plots created successfully!\n")

✅ Method comparison plots created successfully!

cat("📁 All plots saved to results/plots/ directory\n")

📁 All plots saved to results/plots/ directory

Multi-Scenario Analysis

This section creates multi-scenario dose-response curves similar to the reference code.

# Create multi-scenario analysis
cat("\n=== Creating Multi-Scenario Analysis ===\n")

=== Creating Multi-Scenario Analysis ===

# Define different scenarios with varying parameters
scenarios_data <- list(
  list(
    toxicity = c(0.1, 0.18, 0.35, 0.40, 0.50),
    efficacy = c(0.35, 0.35, 0.37, 0.39, 0.39),
    utility = c(0.27, 0.23, 0.10, 0.13, 0.17)
  ),
  list(
    toxicity = c(0.05, 0.15, 0.25, 0.35, 0.50),
    efficacy = c(0.10, 0.35, 0.35, 0.38, 0.39),
    utility = c(0.07, 0.22, 0.22, 0.12, 0.06)
  ),
  list(
    toxicity = c(0.02, 0.06, 0.10, 0.20, 0.35),
    efficacy = c(0.05, 0.10, 0.35, 0.35, 0.40),
    utility = c(0.03, 0.07, 0.28, 0.22, 0.13)
  )
)

# Create multi-scenario plot
multi_scenario_plot <- plot_multi_scenario_curves(
  scenarios_data,
  title = "Dose-Response Curves Across Scenarios",
  file_path = "results/plots/multi_scenario_analysis.png"
)

Scale for y is already present.
Adding another scale for y, which will replace the existing scale.

print(multi_scenario_plot)

cat("✅ Multi-scenario analysis completed!\n")

✅ Multi-scenario analysis completed!

Calibration Framework

This section demonstrates the calibration framework for optimizing trial parameters.

Setup Calibration

# Use absolute paths for calibration functions
project_root <- "/Users/jz/Development/DoseFinding"

# Source calibration functions
source(file.path(project_root, "src/optimization/poc_calibration.R"))
source(file.path(project_root, "src/optimization/early_termination_calibration.R"))
source(file.path(project_root, "src/utils/calibration_plots.R"))

# Set up output directory for calibration results
calibration_output_dir <- "results/notebook_calibration"
dir.create(calibration_output_dir, showWarnings = FALSE, recursive = TRUE)

PoC Calibration

Calibrate the PoC threshold to achieve target detection rates in null scenarios.

# Run PoC calibration with reduced simulations for notebook
cat("Running PoC calibration...\n")

Running PoC calibration...

poc_results <- run_quick_calibration(
  target_rate = 0.10,
  n_simulations = 100  # Reduced for notebook
)

Running quick calibration (reduced simulations for testing)...
Starting PoC calibration...
Target detection rate: 0.1 
Number of simulations per C_poc: 100 
C_poc range: 0.7 to 0.95 

Progress: 1/6 - Testing C_poc = 0.700

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

  PoC detection rate = 0.000 (95% CI: [0.000, 0.036])

Progress: 2/6 - Testing C_poc = 0.750

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.75 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

  PoC detection rate = 0.000 (95% CI: [0.000, 0.036])

Progress: 3/6 - Testing C_poc = 0.800

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.8 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

  PoC detection rate = 0.000 (95% CI: [0.000, 0.036])

Progress: 4/6 - Testing C_poc = 0.850

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.85 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

  PoC detection rate = 0.000 (95% CI: [0.000, 0.036])

Progress: 5/6 - Testing C_poc = 0.900

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

  PoC detection rate = 0.000 (95% CI: [0.000, 0.036])

Progress: 6/6 - Testing C_poc = 0.950

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.95 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 
Utilities: 51.51 
Selected dose: 2 
Selected utility: 51.51 
PoC validated: FALSE 
Max PoC probability: 0 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

  PoC detection rate = 0.000 (95% CI: [0.000, 0.036])

=== CALIBRATION COMPLETE ===
Optimal C_poc = 0.700
Achieved detection rate = 0.000 (target: 0.100)
Difference from target = 0.100
============================

# Display results
cat("PoC Calibration Results:\n")

PoC Calibration Results:

cat("Optimal C_poc =", poc_results$optimal_c_poc, "\n")

Optimal C_poc = 0.7 

cat("Achieved rate =", round(poc_results$optimal_rate, 3), "\n")

Achieved rate = 0 

cat("Target rate =", poc_results$target_rate, "\n")

Target rate = 0.1 

# Create calibration curve
poc_plot <- plot_poc_calibration_curve(
  poc_results,
  target_rate = 0.10,
  save_path = file.path(calibration_output_dir, "poc_calibration_curve.png")
)

Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.

Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
ℹ Please use the `linewidth` argument instead.

Warning: Use of `data$poc_detection_rate` is discouraged.
ℹ Use `poc_detection_rate` instead.

Warning: Use of `data$c_poc` is discouraged.
ℹ Use `c_poc` instead.

Warning in geom_point(aes(x = optimal_c_poc, y = data$poc_detection_rate[data$c_poc == : All aesthetics have length 1, but the data has 6 rows.
ℹ Please consider using `annotate()` or provide this layer with data containing
  a single row.

PoC calibration curve saved to: results/notebook_calibration/poc_calibration_curve.png 

print(poc_plot)

Warning: Use of `data$poc_detection_rate` is discouraged.
ℹ Use `poc_detection_rate` instead.

Warning: Use of `data$c_poc` is discouraged.
ℹ Use `c_poc` instead.

Warning in geom_point(aes(x = optimal_c_poc, y = data$poc_detection_rate[data$c_poc == : All aesthetics have length 1, but the data has 6 rows.
ℹ Please consider using `annotate()` or provide this layer with data containing
  a single row.

Early Termination Calibration

Calibrate early termination parameters to achieve target termination rates in unfavorable scenarios.

# Run early termination calibration with reduced simulations for notebook
cat("Running early termination calibration...\n")

Running early termination calibration...

early_term_results <- run_quick_early_termination_calibration(
  target_rate = 0.80,
  n_simulations = 100  # Reduced for notebook
)

Running quick early termination calibration (reduced simulations for testing)...
Starting early termination calibration...
Target termination rate: 0.8 
Scenario type: unfavorable 
Threshold type: c_T 
Number of simulations per threshold: 100 
Threshold range: 0.8 to 0.95 

Progress: 1/4 - Testing c_T = 0.800

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.8 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===

  Early termination rate = 1.000 (95% CI: [0.964, 1.000])

Progress: 2/4 - Testing c_T = 0.850

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.85 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===

  Early termination rate = 1.000 (95% CI: [0.964, 1.000])

Progress: 3/4 - Testing c_T = 0.900

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.9 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===

  Early termination rate = 1.000 (95% CI: [0.964, 1.000])

Progress: 4/4 - Testing c_T = 0.950

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.571 0.676 0.744 
Summary: Efficacy marginal means: 0.358 0.524 0.712 
Summary: Immune response means: 0.289 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.05 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.83 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.8 )
Dose 2 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.8 )
Dose 3 : P(Tox <  0.3 ) =  0 (Threshold:  0.95 ) P(Eff >  0.2 ) =  1 (Threshold:  0.9 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.8 )
--- End Admissibility Check ---
Admissible set: 
Workflow: Step 4 - Early Termination Check

--- EARLY TERMINATION TRIGGERED ---
Reason: Admissible set is empty (no doses meet safety/efficacy criteria)
Trial will terminate without selecting an Optimal Dose
--- END EARLY TERMINATION ---


=== TRIAL TERMINATION SUMMARY ===
Trial terminated early at stage: 1 
Reason: Empty admissible set 
No Optimal Dose selected
=== END TRIAL TERMINATION ===

  Early termination rate = 1.000 (95% CI: [0.964, 1.000])

=== EARLY TERMINATION CALIBRATION COMPLETE ===
Optimal c_T = 0.800
Achieved termination rate = 1.000 (target: 0.800)
Difference from target = 0.200
==============================================

# Display results
cat("Early Termination Calibration Results:\n")

Early Termination Calibration Results:

cat("Optimal", early_term_results$threshold_type, "=", early_term_results$optimal_threshold, "\n")

Optimal c_T = 0.8 

cat("Achieved rate =", round(early_term_results$optimal_rate, 3), "\n")

Achieved rate = 1 

cat("Target rate =", early_term_results$target_rate, "\n")

Target rate = 0.8 

# Create calibration curve
early_term_plot <- plot_early_termination_curve(
  early_term_results,
  target_rate = 0.80,
  save_path = file.path(calibration_output_dir, "early_termination_calibration_curve.png")
)

Warning: Use of `data$termination_rate` is discouraged.
ℹ Use `termination_rate` instead.

Warning: Use of `data$threshold` is discouraged.
ℹ Use `threshold` instead.

Warning in geom_point(aes(x = optimal_threshold, y = data$termination_rate[data$threshold == : All aesthetics have length 1, but the data has 4 rows.
ℹ Please consider using `annotate()` or provide this layer with data containing
  a single row.

Early termination curve saved to: results/notebook_calibration/early_termination_calibration_curve.png 

print(early_term_plot)

Warning: Use of `data$termination_rate` is discouraged.
ℹ Use `termination_rate` instead.

Warning: Use of `data$threshold` is discouraged.
ℹ Use `threshold` instead.

Warning in geom_point(aes(x = optimal_threshold, y = data$termination_rate[data$threshold == : All aesthetics have length 1, but the data has 4 rows.
ℹ Please consider using `annotate()` or provide this layer with data containing
  a single row.

Combined Performance Curves

Visualize both calibration results together.

# Create combined calibration data
combined_calibration_data <- list(
  poc_calibration = poc_results,
  termination_calibration = early_term_results
)

# Create combined performance curves
combined_plot <- plot_threshold_performance_curves(
  combined_calibration_data,
  save_path = file.path(calibration_output_dir, "combined_performance_curves.png")
)

Combined performance curves saved to: results/notebook_calibration/combined_performance_curves.png 

print(combined_plot)

Calibration Summary

# Create summary table
calibration_summary <- data.frame(
  Parameter = c("C_poc (PoC)", "C_T (Early Termination)", "PoC Target", "PoC Achieved", 
                "Early Termination Target", "Early Termination Achieved"),
  Value = c(
    round(poc_results$optimal_c_poc, 3),
    round(early_term_results$optimal_threshold, 3),
    poc_results$target_rate,
    round(poc_results$optimal_rate, 3),
    early_term_results$target_rate,
    round(early_term_results$optimal_rate, 3)
  )
)

# Display summary table
kable(calibration_summary, caption = "Calibration Summary")

Calibration Summary

Parameter	Value
C_poc (PoC)	0.7
C_T (Early Termination)	0.8
PoC Target	0.1
PoC Achieved	0.0
Early Termination Target	0.8
Early Termination Achieved	1.0

Summary

This notebook demonstrates the Bayesian dose-finding trial simulation with modern, publication-ready visualizations inspired by the reference code. The plots include:

• Dose-response curves with toxicity, efficacy, and utility
• Posterior summaries with modern styling
• Allocation analysis showing participant distribution
• Method comparisons for performance evaluation
• Multi-scenario analysis for parameter sensitivity
• Calibration framework for optimizing trial parameters

All plots use consistent color schemes and professional styling suitable for academic publications and regulatory submissions.

```